ANS:A - T

The molecular velocity of a gas is proportional to the square root of the absolute temperature (T) of the gas. Therefore, it is proportional to √T. The relationship between the molecular velocity of a gas and the absolute temperature (T) is described by the kinetic theory of gases. According to this theory, the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. The kinetic energy of a gas molecule is given by the formula: 𝐾𝐸=12𝑚𝑣2KE=21​mv2 Where:

• KE represents the kinetic energy,
• m is the mass of the gas molecule, and
• v is the velocity of the gas molecule.

Now, if we rearrange this equation to solve for velocity (v), we get: 𝑣=2⋅𝐾𝐸𝑚v=m2⋅KE​​ Since the average kinetic energy is directly proportional to the absolute temperature (T), we can substitute KE with a term proportional to T. Let's denote this constant of proportionality as k: 𝐾𝐸=𝑘𝑇KE=kT Therefore, the equation for velocity becomes: 𝑣=2⋅𝑘𝑇𝑚v=m2⋅kT​​ Now, we can see that the velocity (v) is proportional to the square root of the absolute temperature (T), as the mass (m) of the gas molecules is constant. So, the molecular velocity of a gas is indeed proportional to the square root of the absolute temperature (T), which is represented mathematically as 𝑇T​.